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Published March 31, 2020 | Submitted + Published
Journal Article Open

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches

Abstract

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations.

Additional Information

© 2020 Published under license by AIP Publishing. Submitted: 5 January 2020; Accepted: 6 March 2020; Published Online: 30 March 2020. We acknowledge support from the Department of Energy under Award No. DE-FOA-0001912 and the National Science Foundation under Award No. CHE-1611581. P.S. acknowledges a German Research Foundation (DFG) postdoctoral fellowship. Computational resources were provided by the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

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August 19, 2023
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